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gamThresholds_final_KA_2016.10.19.R
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gamThresholds_final_KA_2016.10.19.R
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rm(list = ls())
###############
# Script Info #
###############
# PURPOSE: Thresholds from a GAMM or GAM using maximum entropy bootstrapping
# AUTHOR: Scott Large 2013 (revised 2016 by Gavin Fay and Kelly Andrews)
# REVIEWED BY:
# VERSION: 20
#########################
# SPECIAL INSTRUCTIONS: #
#########################
#INSERT THE "DATASET" BEING USED BELOW (EITHER "1996" OR "2003" OR an abbreviated name of your dataset - this will be used to decide which indicators and pressures to use, to create results folders and this name will be inserted in the file name of results and figures)
dataset <- 2003 #use either the "1996" or "2003" datasets for the California Current indicators. 1996 dataset includes data from 1996-2014; truncated dataset contains data from 2003-2102 - this is used in comparison with gradient forest dataset
test <- "no" #use either "yes" or "no". For full data analysis, use "no". If you want to test code with one combination of pressure/response indicators then use "yes". This will trigger ifelse statements to identify "resp" and "dri" used in the full dataset in lines ~83-139 below.
######################
# CHANGES/ ADDITIONS #
######################
# Need to add: Gaussian bootstrap method for GAM; can't seem to get it to work right
# Done:
############
# PACKAGES #
############
library(meboot)
library(mgcv)
library(reshape2)
library(mvtnorm)
library(MASS)
library(nlme)
library(lme4)
#
##################
# Set up folders #
##################
#setwd("D:\\My Documents\\Manuscripts\\Reference Points\\GAMM results/")
setwd("~/Desktop/codeforreferencepointspaper/")
data.dir <- "data/"
results.dir <- "output/"
if (file.exists(results.dir)==FALSE) dir.create(results.dir)
results.dir <- paste0("output/",dataset,"/")
#7/23/15, GFAY - make the output directory if not there yet.
if (file.exists(results.dir)==FALSE) dir.create(results.dir)
#
######################
# Load any functions #
######################
#
#
AICc <- function(mod) {
K.c <- mod$rank
N.c <- length(mod$residuals)
AIC.c <- round(mod$aic + (2*K.c*(K.c+1)/(N.c-K.c-1)),3)
return(AIC.c)
}
#############
# Load data #
#############
set.seed(627)
ifelse(dataset==1996,{
cc <- read.csv("data/1996.2014.reference.points.data.csv")
ccALL <- cc
ccALL$year <- as.numeric(ccALL$year)
# Wide df with columns as variables
dat.full <- dcast(ccALL, year ~ timeseries, value.var = "value")
##############################################################
### Use these response and drivers for the 1996-2014 data ####
##############################################################
#### Three relationships (GF_spp_density * NPGO_summer and N_Cop_Anom_winter * NOI_summer) have an error:
#### Error in lme.formula(y ~ X - 1, random = rand, data = strip.offset(mf), : nlminb problem,
#### convergence error code = 1 message = singular convergence (7)
ifelse(test=="no",{
resp <- c(rep("CA sea lion pup growth",16),rep("CA sea lion pup production",16),
rep("Groundfish mean trophic level",16), rep("Groundfish species density",16),
rep("Groundfish species richness",16), rep("Groundfish Simpson diversity",16),
rep("Copepod anomaly summer",16), rep("Copepod anomaly winter",16),
rep("Scavenger ratio",16))
dri <- c(rep(c("Atmospheric pollution","Commercial shipping activity","Dredging",
"Groundfish landings","Habitat modification","Inorganic pollution",
"Invasive species","Nutrient input","Organic pollution","Total fisheries landings",
"NOI summer","NOI winter","NPGO summer","NPGO winter","PDO summer","PDO winter"),9))
}, #end "no" statement
{
#TO TEST CODE WITH ONE COMBINATION. ONLY USED IF "test" is set to "yes" in Instructions at top of code
resp <- c(rep("Copepod anomaly winter",1))
dri <- c(rep(c("Habitat modification"),1))
#resp <- c(rep("CA sea lion pup production",1))
#dri <- c(rep(c("NOI summer"),1))
} #end of test code statement
)
}, #end of 1996 variables
{
cc <- read.csv("data/2003.2012.reference.points.data.csv")
ccALL <- cc
ccALL$year <- as.numeric(ccALL$year)
# Wide df with columns as variables
dat.full <- dcast(ccALL, year ~ timeseries, value.var = "value")
#############################################################
### Use these response and drivers for the 2003-2012 data ####
##############################################################
###WHEN USING THE 2003-2012 DATA AND WHEN ALL COMBINATIONS ARE INCLUDED, TWO RELATIONSHIPS GIVE THE FOLLOWING
###ERROR: "Error in lme.formula(y ~ X - 1, random = rand, data = strip.offset(mf), :nlminb problem,
###convergence error code = 1 message = singular convergence (7)"
###THOSE TWO RELATIONSHIPS WERE (N_Cop_Anom_summer * Atmospheric_pollution) and (N_Cop_Anom_summer *
###NOI_summer)#####
ifelse(test=="no",{
resp <- c(rep("CA sea lion pup growth",14),rep("CA sea lion pup production",14),
rep("Groundfish mean trophic level",14), rep("Groundfish species density",14),
rep("Groundfish species richness",14), rep("Groundfish Simpson diversity",14),
rep("Copepod anomaly summer",14), rep("Copepod anomaly winter",14),
rep("Scavenger ratio",14))
dri <- c(rep(c("Atmospheric pollution","Commercial shipping activity","Dredging",
"Groundfish landings","Habitat modification","Inorganic pollution",
"Invasive species","Total fisheries landings",
"NOI summer","NOI winter","NPGO summer","NPGO winter","PDO summer","PDO winter"),9))
}, #end test=="no" statement
{
#TO TEST CODE WITH ONE COMBINATION, UNCOMMENT THE FOLLOWING TWO LINES:
resp <- c(rep("CA sea lion pup production",1))
dri <- c(rep(c("PDO summer"),1))
} #end of test=="yes" part
) #end test loop
} #end of 2003 variables
) #end of ifelse for which dataset (1996 or 2003) used
allSummary <- data.frame()
allMagnitude <- data.frame()
allMag.means <- data.frame()
for (imod in 1:length(resp)) #loop analyses over all possible response/driver combinations
{
#imod=1
resp.name <- resp[imod]
dri.name <- dri[imod]
dat.cut <- dat.full[colnames(dat.full) %in% c("year", resp.name, dri.name)]
dat.cut <- dat.cut[apply(dat.cut, 1, function(x)!any(is.na(x))),]
#
myresponse <- dat.cut[[resp.name]]
mydriver <- dat.cut[[dri.name]]
ts.length <- dat.cut$year
if(length(mydriver)>0 & length(myresponse)>0)
{
#
#####################
# Fit the GAM model #
#####################
sp.len <- 200 # Spline length
nb <- 1000 # Number of bootstrap replicates
gam.mat <- matrix(nrow=sp.len, ncol=nb) ## create a matrix to be filled with bootstrapped splines (200 x 1000)
dif1 <- 1 # First derivative
dif2 <- 2 # Second derivative
ks <- 4 #If ks=3, no relationships have edf values > 2.0
rand <- rep(1,length(myresponse))
#Step 1. Fit GAM to answer whether temporal autocorrelation is important? Use the residuals from the gam and a log likelihood ratio test to calculate the "P.ac" value. A significant p.ac value suggests a model with autocorrelated error structure explains more of the variation in the residuals of the gam model than a model without autocorrelated error structure. Thus, using a GAMM is necessary to account for autocorrelation in the time series...use GAMM if p.ac < 0.05. If p.ac > 0.05, then GAM will be used to look for non-linearities, so this code will also fit the model and provide selection criteria (i.e. edf, GCV and AIC scores from GAM and Linear model (linear) to compare)
gam1 <- gam(myresponse ~ s(mydriver, bs= "tp",k = ks), optimMmethod="GCV.Cp",se = T)
linear <- gam(myresponse ~ mydriver, method = "GCV.Cp", se = T)
dev.resid <- residuals(gam1,type='deviance')
lme1 <- lme(dev.resid~1,random=~1|rand,correlation=corAR1(form=~ts.length),method='ML')
lm1 <- lm(dev.resid~1)
p.ac <- 1-pchisq(2*(logLik(lme1)[1]-logLik(lm1)[1]),2)
delta.GCV.gam.lm <- summary(gam1)$sp.criterion - summary(linear)$sp.criterion #A negative value means the GAM with a smoother is a better model than the linear model
delta.AIC.gam.lm <- AICc(gam1) - AICc(linear) #A negative value means the GAM with a smoother is a better model than the linear model
dev.diff.gam.lm <- summary(gam1)$dev.expl-summary(linear)$dev.expl
#Step 2. Fit GAMM to get selection criteria for relationships where p.ac < 0.05 (i.e. edf and AIC) and calculate deviance explained by GAMM ("gamm.dev.expl" below)
try(gamm <- gamm(myresponse ~ s(mydriver, bs= "tp",k = ks), optimMmethod="GCV.Cp",
se = T,correlation=corAR1(form=~ts.length)))
if (length(gamm)==0)
{
print(imod)
gamm <- gamm(myresponse ~ s(mydriver),se = T,correlation=corAR1(form=~ts.length))
}
#Fit null model to compute deviance explained by gamm
null <- glmmPQL(myresponse ~ 1,random=list(rand=~1),family='gaussian')
dr <- sum(residuals(gamm$gam)^2)
dn0 <- sum(residuals(null)^2)
gamm.dev.expl <- (dn0-dr)/dn0
#Step 3. Fit linear model with autocorrelation (LMAC) to get selection criteria (i.e. AIC) and calculate deviance explained by LMAC ("lmac.dev.expl" below).
try(lmac <- gamm(myresponse ~ mydriver, optimMmethod="GCV.Cp",
se = T,random=list(rand=~1),correlation=corAR1(form=~ts.length)))
if (length(lmac)==0)
{
print(imod)
lmac <- gamm(myresponse ~ mydriver,random=list(rand=~1),se = T,
correlation=corAR1(form=~ts.length))
}
dr2 <- sum(residuals(lmac$gam)^2)
lmac.dev.expl <- (dn0-dr2)/dn0
# Calculate difference in deviance and AIC between GAMM and LMAC ("dev.diff.gamm.lmac" and "delta.AIC.gamm.lmac" respectively below).
dev.diff.gamm.lmac <- gamm.dev.expl-lmac.dev.expl
delta.AIC.gamm.lmac <- summary(gamm$lme)$AIC-summary(lmac$lme)$AIC #A negative value means the GAMM is a better model than the linear model with temporal autocorrelation
# # Pull out relevant model outputs:
#FOR GAMM:
summary.gamm <- as.data.frame(cbind("GAMM", # Model name
resp.name, # Response variable
dri.name, # Pressure variable
summary(gamm$lme)$AIC, # AICc
summary(gamm$lme)$logLik, # log likelihood
gamm.dev.expl, # Deviance explained by gamm
summary(gamm$gam)$edf, # estimated degrees of freedom
summary(gamm$gam)$s.pv, # p-value of the smoother
summary(gamm$gam)$r.sq, # R-squared value
NA, # placeholder for GCV value used in gam
NA, # placeholder for delta.GCV data used as selection criteria for gams
as.numeric(p.ac), # p-value of log likelihood ratio test that tests whether the residuals from the gam are better explained by a model with or without temporal autocorrelation; p.ac values < 0.05 suggest autocorrelation is important and a gamm (instead of a gam) should be used.
delta.AIC.gamm.lmac, # delta AIC between gamm and lmac models; negative value means gamm is a better model than LMAC
dev.diff.gamm.lmac # difference in deviance explained between gamm and lmac
))
colnames(summary.gamm)<- c("MODEL", "RESPONSE", "DRIVER", "AICc", "logLik","dev.expl", "edf", "Pvalue","R-squared","GCV","delta.GCV","p.ac","delta.AIC","diff.dev.expl")
#FOR Linear Model with Auto Correlation
summary.lmac <- as.data.frame(cbind("LMAC", # Model name
resp.name, # Response variable
dri.name, # Pressure variable
summary(lmac$lme)$AIC, # AICc
summary(lmac$lme)$logLik, # log likelihood
lmac.dev.expl, # Deviance explained by LMAC
summary(lmac$gam)$residual.df, # residual degrees of freedom
summary(lmac$gam)$p.pv[[2]], # p-value of the null hypothesis
summary(lmac$gam)$r.sq, # R-squared value
NA, # placeholder for GCV value used in gam
NA, # placeholder for delta.GCV data used as selection criteria for gams
NA, # placeholder for p.ac for gamm
NA, # placeholder for delta AIC
NA # placeholder for diff in deviance explained
))
colnames(summary.lmac)<- c("MODEL", "RESPONSE", "DRIVER", "AICc", "logLik","dev.expl", "edf", "Pvalue","R-squared","GCV","delta.GCV","p.ac","delta.AIC","diff.dev.expl")
#FOR GAM
summary.gam1 <- as.data.frame(cbind("GAM", # Model name
resp.name, # Response variable
dri.name, # Pressure variable
AICc(gam1), # AICc
logLik(gam1), # Log likelihood
summary(gam1)$dev.expl, # deviance explained by gam
summary(gam1)$edf, # estimated degrees of freedom
summary(gam1)$s.pv, # p-value of the smoother
summary(gam1)$r.sq, # R-squared value
summary(gam1)$sp.criterion, # GCV value for gam
delta.GCV.gam.lm, # GAM GCV score minus LM GCV score; #A negative value means the GAM with a smoother is a better model than the linear model
NA, # placeholder for p.ac value for gamm
delta.AIC.gam.lm, # delta AICc between gam and linear model; a negaive value means the GAM with a smoother is a better model than the linear model
dev.diff.gam.lm # Difference in deviance explained between the gam and the linear model
))
colnames(summary.gam1)<- c("MODEL", "RESPONSE", "DRIVER", "AICc", "logLik","dev.expl", "edf", "Pvalue","R-squared","GCV","delta.GCV","p.ac","delta.AIC","diff.dev.expl")
#FOR LINEAR MODEL
summary.linear <- as.data.frame(cbind("Linear", # Model name
resp.name, # Response variable
dri.name, # Pressure variable
AICc(linear), # AICc
logLik(linear), # Log likelihood
summary(linear)$dev.expl, # deviance explained by linear model
summary(linear)$residual.df, # residual degrees of freedom
summary(linear)$p.pv[[2]], # p-value of the null hypothesis
summary(linear)$r.sq, # R-squared value
summary(linear)$sp.criterion, # GCV value for linear model
NA, # placeholder for delta.GCV data used as selection criteria for gams
NA, # placeholder for p.ac for gamm
NA, # placeholder for delta AIC
NA # placeholder for diff in deviance explained
))
colnames(summary.linear)<- c("MODEL", "RESPONSE", "DRIVER", "AICc", "logLik","dev.expl", "edf", "Pvalue","R-squared","GCV","delta.GCV","p.ac","delta.AIC","diff.dev.expl")
### Identify "best model"#####
### 1a) Is p.ac <= 0.05? If yes, keep and evaluate selection criteria between GAMM and LMAC as best model.If no, move to step 2.
### 1b) Is GAMM edf > 2.0 for GAMM? If yes, keep. If no, LMAC is best.
### 1c) Is delta.AIC > 2.0 between GAMM and LMAC. If yes, GAMM is best. If no, LMAC is most parsimonious.
### 2a) If p.ac > 0.05, then revert to GAM model and ask if edf of GAM > 2.0? If yes, keep GAM. If no, linear model is best model.
### 2b) Is GCV minimized in GAM compared to Linear model? If delta.GCV.gam.lm is negative then keep GAM. If delta.GCV.gam.lm is positive then linear model is best.
### 2c) Is deltaAIC > 2.0 for GAM? If yes, then GAM is best model. If no, then linear model is best model.
summary.gamm$best.model = ifelse(as.numeric(as.character(summary.gamm$p.ac))<=0.05,
ifelse(as.numeric(as.character(summary.gamm$edf))>=1.99,
ifelse(as.numeric(as.character(summary.gamm$delta.AIC))>=2.0,"yes","no"),"no"),"no")
summary.lmac$best.model = ifelse(as.numeric(as.character(summary.gamm$p.ac))<=0.05,
ifelse(as.numeric(as.character(summary.gamm$edf))>=1.99,
ifelse(as.numeric(as.character(summary.gamm$delta.AIC))>=2.0,"no","yes"),"yes"),"no")
summary.gam1$best.model = ifelse(as.numeric(as.character(summary.gamm$p.ac))>0.05,
ifelse(as.numeric(as.character(summary.gam1$edf))>1.99,
ifelse(as.numeric(as.character(summary.gam1$delta.GCV))<0,
ifelse(as.numeric(as.character(summary.gam1$delta.AIC))<=-2.0,"yes","no"),"no"),"no"),"no")
summary.linear$best.model = ifelse(as.numeric(as.character(summary.gamm$p.ac))>0.05,
ifelse(as.numeric(as.character(summary.gam1$edf))<1.99,"yes",
ifelse(as.numeric(as.character(summary.gam1$delta.GCV))>0,"yes",
ifelse(as.numeric(as.character(summary.gam1$delta.AIC))<=-2.0,"no","yes"))),"no")
allSummary <- rbind(allSummary, summary.gamm, summary.lmac, summary.gam1,
summary.linear)
} #end if statement for doing the models
} ##imod loop (relevant combinations of driver/responses)
allSummary <- cbind(rownames(allSummary),allSummary)
colnames(allSummary) <- c("PICK#", "MODEL", "RESPONSE", "DRIVER", "AICc", "logLik","dev.expl", "edf", "Pvalue","R-squared","GCV","delta.GCV","p.ac","delta.AIC","diff.dev.expl","best.model")
#Output all relevant model output to data file
bestList <- allSummary
if(test=="yes")
{row.i <- 1
}
if(test=="no")
{
write.table(allSummary,paste0(results.dir,paste0(dataset,'.all.models.summary.out')),row.names=FALSE)
write.csv(allSummary,paste(results.dir,paste0(dataset,".all.models.summary.out.csv")),row.names=F)
resp.name <- NULL
dri.name <- NULL
row.i <- 1
pick.gamm <- which(allSummary$best.model=="yes" & allSummary$MODEL=="GAMM")
pick.gam <- which(allSummary$best.model=="yes" & allSummary$MODEL=="GAM")
#############################################################################################################
###CODE FOR MAKING PLOTs FOR RELATIONSHIPS THAT SHOWED GAMM WAS THE BEST MODEL (using "pick.gamm" from above)
#############################################################################################################
for(row.i in pick.gamm) {
resp.name <- as.character(bestList$RESPONSE[row.i])
dri.name <- as.character(bestList$DRIVER[row.i])
dat.cut <- dat.full[colnames(dat.full) %in% c("year", resp.name, dri.name)]
dat.cut <- dat.cut[apply(dat.cut, 1, function(x)!any(is.na(x))),]
#
myresponse <- dat.cut[[resp.name]]
mydriver <- dat.cut[[dri.name]]
ts.length <- dat.cut$year
try(gamm <- gamm(myresponse ~ s(mydriver, bs= "tp",k = ks), optimMmethod="GCV.Cp",
se = T,correlation=corAR1(form=~ts.length)))
if (length(gamm)==0)
{
print(imod)
gamm <- gamm(myresponse ~ s(mydriver),se = T,correlation=corAR1(form=~ts.length))
}
ind.fit <- list(mydriver = seq(from = min(mydriver), to = max(mydriver), length.out = sp.len))
pred <- predict.gam(gamm$gam, newdata = ind.fit, type = "response", se.fit = T)
#
gam.data <- data.frame(pred$fit,
ind.fit$mydriver)
colnames(gam.data) <- c("response","driver")
# Bootstrap and subsequent code in a nutshell...
# 1) take a random sample of the data 1000 times
# 2) take GAM of each bootstrap replicate (br)
# 3) Take the 1st and 2nd derivative of each br
# 4) When 95% of the 1st or 2nd derivative replicates are greater or less than zero, we have a significant
# trend (1st derivative), or threshold (2nd derivative).
#
# Note on maximum entropy bootstrap:
# Bootstrapping is a nonparametric alternative for assessing the
# uncertainty of a linear trend in the presence
# of autocorrelation. Maximum entropy bootstrap allows
# us to construct a set of replicates of the original series
# to be used for inference while retaining the temporal
# dependence structure of the original series in the resampling process
#
respboot <- meboot(myresponse, reps = nb, trim = 0.1)$ens
drivboot <- meboot(mydriver, reps = nb, trim = 0.1)$ens
resids <- myresponse-gamm$gam$fitted
# sample multivariate normal for use in gaussian process regression bootstrap
phi = coef(gamm$lme$modelStruct$corStruct,unconstrained=FALSE)
dist <- matrix(0,nrow=length(resids),ncol=length(resids))
for (i in 1:nrow(dist)) for (j in 1:ncol(dist)) dist[i,j] = abs(j-i)
dist <- phi^dist
resids.use <- rmvnorm(nb,rep(mean(resids),length(resids)),sigma=var(resids)*dist,method="chol")
for (i in 1:nb)
{
#use next line if just doing residual bootstrap - for "gam" calls
#respboot[,i] <- gamm$gam$fitted + sample(resids,length(resids),replace=TRUE)
#use next line if doing gaussian process residual bootstrap - for "gamm" calls
respboot[,i] <- gamm$gam$fitted + resids.use[i,]
drivboot[,i] <- mydriver
}
#
gam.mat <- matrix(ncol = nb, nrow = sp.len)
for(i in 1:nb) {
resp.i <- respboot[,i]
driv.i <- drivboot[,i]
#gam.i <- gam(resp.i ~ s(driv.i, bs = "tp", k = ks), method = "GCV.Cp", se = T)
# gam.i <- gamm(resp.i ~ s(driv.i, bs= "tp",k = ks), optimMmethod="GCV.Cp",
# se = T,correlation=corAR1(form=~ts.length))
gam.i <- NULL
try(gam.i <- gamm(resp.i ~ s(driv.i,k=ks,bs='tp'),optimMethod="GCV.Cp",
se = T,correlation=corAR1(form=~ts.length),random=NULL),silent=TRUE)
if (length(gam.i)!=0)
{
newdata.i <- list(driv.i = seq(from = min(driv.i),
to = max(driv.i),
length.out = sp.len))
gam.mat[,i] <- predict.gam(gam.i$gam, newdata = newdata.i, type = "response", se.fit = T)$fit
}
}
#
#######################
# CI of GAM bootstrap #
#######################
ci <- matrix(nrow= 2, ncol= sp.len) ## create a matrix to be filled with bootstrapped CI
rownames(ci)<-c("lower","upper")
for(j in 1:sp.len) {
IC <- quantile(gam.mat[j,], c(0.025, 0.975),na.rm=TRUE)
ci[,j]<-rbind(IC[1], IC[2])
}
#############################
# 1st Derivative Estimation #
#############################
dif1.line<-diff(gam.data$response, difference=1) # Actual 1st deriv estimate from original smoother
deriv.matrix.1<-matrix(nrow=sp.len-dif1, ncol=nb) ## create a matrix to for the 1st deriv estimates
for(k in 1:nb) {
derivi<-gam.mat[,k]
deriv.response<-diff(derivi, difference=dif1)
driver.len<-length(mydriver)-dif1
deriv.object <- cbind(deriv.response,driver.len)
deriv.matrix.1[,k]<-deriv.object[,1]
}
# CI of 1st derivative
dif1.len <- sp.len-dif1
ci1 <- matrix(nrow= 2, ncol= dif1.len) ## create a matrix to be filled with bootstrapped CI
rownames(ci1) <- c("lower","upper")
#
for(l in 1:dif1.len) {
IC<-quantile(deriv.matrix.1[l,], c(0.025, 0.975),na.rm=TRUE)
ci1[,l]<-rbind(IC[1], IC[2])
}
#
#############################
# 2nd Derivative Estimation #
#############################
temp <- diff(gam.data$response,difference=1)
dif2.line<-diff(temp, difference=1) # Actual 2nd deriv estimate from original smoother
deriv.matrix.2<-matrix(nrow=sp.len-dif2, ncol=nb) ## create a matrix to for the 2nd deriv estimates
for(m in 1:nb) {
derivi<-gam.mat[,m]
temp <- diff(derivi, difference=1)
deriv.response<-diff(temp, difference=1)
driver.len<-length(mydriver)-dif2
deriv.object <- cbind(deriv.response,driver.len)
deriv.matrix.2[,m]<-deriv.object[,1]
}
# CI of 2nd derivative
dif2.len<-sp.len-dif2
ci2<-matrix(nrow= 2, ncol= dif2.len) ## create a matrix to be filled with bootstrapped CI
rownames(ci2)<-c("lower","upper")
#
for(n in 1:dif2.len) {
IC<-quantile(deriv.matrix.2[n,], c(0.025, 0.975),na.rm=TRUE)
ci2[,n]<-rbind(IC[1], IC[2])
}
#
# CI of response
lower <- min(ci[1, ])
upper <- max(ci[2, ])
lower1 <- min(ci1[1, ])
upper1 <- max(ci1[2, ])
lower2 <- min(ci2[1, ])
upper2 <- max(ci2[2, ])
#
CI.table<-matrix(nrow=2, ncol=3, data=c(upper,
lower,
upper1,
lower1,
upper2,
lower2),
dimnames=list(c("UPPER", "LOWER"),
c("GAM","FIRST","SECOND")))
CI.mat <- data.frame(CI.table)
#
###################
# Make some plots #
###################
#
changepts.lower1 <- seq(1, length(dif1.line)) [ci1["lower", ] > 0]
changepts.upper1 <- seq(1, length(dif1.line)) [ci1["upper", ] < 0]
changepts.lower2 <- seq(1, length(dif2.line)) [ci2["lower", ] > 0]
changepts.upper2 <- seq(1, length(dif2.line)) [ci2["upper", ] < 0]
#
driver1 <- gam.data$driver[-1]
driver2 <- gam.data$driver[-c(1,2)]
#
####################################################################################
## PLOTS function with 2nd derivative arrow in one-panel plot##
####################################################################################
# Will make a plot in your "figures directory"
der.plot <- paste0(results.dir, paste0(dataset,".",resp.name, "-", dri.name, ".gamm.png"))
png(file = der.plot, width = 5, height = 3, units = "in", res = 600)
#
#########################################
# Figure: GAM pressure-response plot #
#########################################
par(mfg= c(1,1),
mar=c(2.75,2.75,0.5,0.25),
mgp=c(0,0.25,0),
cex= 0.75,
tck=-0.02,
family = "sans")
plot(myresponse ~ mydriver,
#ylim = c(min(CI.mat$GAM[2],myresponse),max(CI.mat$GAM[1],myresponse)),
ylim = c(ifelse(CI.mat$GAM[2] < min(myresponse), CI.mat$GAM[2], min(myresponse)),
ifelse(CI.mat$GAM[1] > max(myresponse), CI.mat$GAM[1], max(myresponse))),
type = "n",
ylab="",
xlab="",
axes = F)
#
dri.ax <- pretty(range(gam.data$driver), 6)
axis(1, dri.ax,cex=1)
mtext(dri.name, side = 1, line = 1.5, cex=1)
#
gam.ax <- pretty(c(CI.mat$GAM[2], CI.mat$GAM[1]), 3)
axis(2, gam.ax,cex=1)
mtext(resp.name, side= 2,line=1.5, cex=1)
#
# Shading 95% CIs
polygon(c(gam.data$driver, rev(gam.data$driver)),
c(ci[2, ], rev(ci[1, ])),
col = gray(0.95),
border = gray(.80))
#
# GAM Line
lines(gam.data$response ~ gam.data$driver, lty =2, lwd=2)
# PLOT DERIVATIVES
points(gam.data$response[ci2["lower", ] > 0] ~ gam.data$driver[ci2["lower", ] > 0],
col = gray(.35), pch = 16)
points(gam.data$response[ci2["upper", ] < 0] ~ gam.data$driver[ci2["upper", ] < 0],
col = gray(.35), pch = 16)
# Add original data points
points(myresponse~mydriver, pch = 16, cex=1, lwd=1)
#text(myresponse~mydriver, labels = as.character(ts.length), cex=.5, offset = 0.6) #adds points with year text
#
#Add dotted line at most probable threshold level of pressure
threshold.df <- data.frame(response = gam.data$response[-c(1,2)], driver2=driver2, dif2=dif2.line,
ci2.upper=ci2["upper",], ci2.lower=ci2["lower",])
threshold.df.upper <- threshold.df[threshold.df$ci2.upper < 0, ]
threshold.upper.mlt <- data.frame(driver2 = threshold.df.upper$driver2[which.min(threshold.df.upper$dif2)],
response = threshold.df.upper$response[which.min(threshold.df.upper$dif2)])
p=length(row.names(threshold.df.upper))
ylim = c(min(CI.mat$GAM[2],myresponse),max(CI.mat$GAM[1],myresponse))
ifelse(ylim[1] > 0,
b <- ylim[1]-((ylim[2]-ylim[1])*0.04),
b <- ylim[1]*1.08)
threshold.df.lower <- threshold.df[threshold.df$ci2.lower > 0, ]
threshold.lower.mlt <- data.frame(driver2 = threshold.df.lower$driver2[which.max(threshold.df.lower$dif2)],
response = threshold.df.lower$response[which.max(threshold.df.lower$dif2)])
threshold.lower.start <- threshold.df.lower[1,2]
threshold.lower.end <- threshold.df.lower[dim(threshold.df.lower)[[1]],2]
q=length(row.names(threshold.df.lower))
if(p!=0)segments(threshold.upper.mlt[[1]],b,threshold.upper.mlt[[1]],threshold.upper.mlt[[2]], lty=3, col = "red", lwd=2)
if(q!=0)segments(threshold.lower.mlt[[1]],b,threshold.lower.mlt[[1]],threshold.lower.mlt[[2]], lty=3, col = "red", lwd=2)
#Add arrows pointing to threshold level of pressure
arr.length <- 0.01*(gam.ax[4] - gam.ax[1]) #make arrow 10% the length of the y-axis
arrhead.length <- 0.1 #make arrowhead
if(p!=0)arrows(x0 = threshold.upper.mlt[[1]], x1 = threshold.upper.mlt[[1]], y0 = b + arr.length,
y1 = b,length=arrhead.length, col = "red", lwd=2)
if(q!=0)arrows(x0 = threshold.lower.mlt[[1]], x1 = threshold.lower.mlt[[1]], y0 = b + arr.length,
y1 = b,length=arrhead.length, col = "red", lwd=2)
box()
dev.off()
##
####################################################################################
## PLOTS function, 1st derivative and 2nd derivative in multi-panel plot##
####################################################################################
# Will make a plot in your "figures directory"
der.plot <- paste0(results.dir, paste0(dataset,".",resp.name, "-", dri.name, ".3.panel.gamm.png"))
png(file = der.plot, width = 90, height = 130, units = "mm", res = 600)
layout(matrix(c(1:3), 3,1, byrow = T),
widths = lcm(8.45), heights = lcm(c(4.95,3.45, 4.45)),
respect = F)
#
#########################################
# Figure A): GAM pressure-response plot #
#########################################
par(mfg= c(1,1),
mar=c(0,2.15,0.5,0.25),
mgp=c(0,0.25,0),
cex= 0.75,
tck=-0.02,
family = "sans")
plot(myresponse ~ mydriver,
#ylim = c(min(CI.mat$GAM[2],myresponse),max(CI.mat$GAM[1],myresponse)),
ylim = c(ifelse(CI.mat$GAM[2] < min(myresponse), CI.mat$GAM[2], min(myresponse)),
ifelse(CI.mat$GAM[1] > max(myresponse), CI.mat$GAM[1], max(myresponse))),
type = "n",
ylab="",
xlab="",
axes = F)
#
dri.ax <- pretty(range(gam.data$driver), 6)
axis(1, dri.ax, labels=F)
#mtext(dri.name, side = 1, line = 1.25, cex = 0.75)
#
gam.ax <- pretty(c(CI.mat$GAM[2], CI.mat$GAM[1]), 3)
axis(2, gam.ax)
mtext(resp.name, side= 2,line=1.5, cex= 0.75)
#
# Shading 95% CIs
polygon(c(gam.data$driver, rev(gam.data$driver)),
c(ci[2, ], rev(ci[1, ])),
col = gray(0.95),
border = gray(.80))
#
# GAM Line
lines(gam.data$response ~ gam.data$driver, lty =2, lwd=2)
# PLOT DERIVATIVES
points(gam.data$response[ci2["lower", ] > 0] ~ gam.data$driver[ci2["lower", ] > 0],
col = gray(.35), pch = 16)
points(gam.data$response[ci2["upper", ] < 0] ~ gam.data$driver[ci2["upper", ] < 0],
col = gray(.35), pch = 16)
# Add original data points
points(myresponse~mydriver, pch = 16, cex=1, lwd=1)
#text(myresponse~mydriver, labels = as.character(ts.length), cex=.5, offset = 0.6) #adds points with year text
#
#Add dotted line at most probable threshold level of pressure
threshold.df <- data.frame(response = gam.data$response[-c(1,2)], driver2=driver2, dif2=dif2.line,
ci2.upper=ci2["upper",], ci2.lower=ci2["lower",])
threshold.df.upper <- threshold.df[threshold.df$ci2.upper < 0, ]
threshold.upper.mlt <- data.frame(driver2 = threshold.df.upper$driver2[which.min(threshold.df.upper$dif2)],
response = threshold.df.upper$response[which.min(threshold.df.upper$dif2)])
p=length(row.names(threshold.df.upper))
ylim = c(min(CI.mat$GAM[2],myresponse),max(CI.mat$GAM[1],myresponse))
ifelse(ylim[1] > 0,
b <- ylim[1]-((ylim[2]-ylim[1])*0.04),
b <- ylim[1]*1.08)
threshold.df.lower <- threshold.df[threshold.df$ci2.lower > 0, ]
threshold.lower.mlt <- data.frame(driver2 = threshold.df.lower$driver2[which.max(threshold.df.lower$dif2)],
response = threshold.df.lower$response[which.max(threshold.df.lower$dif2)])
threshold.lower.start <- threshold.df.lower[1,2]
threshold.lower.end <- threshold.df.lower[dim(threshold.df.lower)[[1]],2]
q=length(row.names(threshold.df.lower))
if(p!=0)segments(threshold.upper.mlt[[1]],b,threshold.upper.mlt[[1]],threshold.upper.mlt[[2]], lty=3, col = "red", lwd=2)
if(q!=0)segments(threshold.lower.mlt[[1]],b,threshold.lower.mlt[[1]],threshold.lower.mlt[[2]], lty=3, col = "red", lwd=2)
#Add arrows pointing to threshold level of pressure
arr.length <- 0.01*(gam.ax[4] - gam.ax[1]) #make arrow 10% the length of the y-axis
arrhead.length <- 0.1 #make arrowhead
if(p!=0)arrows(x0 = threshold.upper.mlt[[1]], x1 = threshold.upper.mlt[[1]], y0 = b + arr.length,
y1 = b,length=arrhead.length, col = "red", lwd=2)
if(q!=0)arrows(x0 = threshold.lower.mlt[[1]], x1 = threshold.lower.mlt[[1]], y0 = b + arr.length,
y1 = b,length=arrhead.length, col = "red", lwd=2)
# Add legend
legend("topleft",
legend="a)",
bty = "n",
box.lwd=0,
box.col="white")
#
box()
########################
# Figure B) s'(X) plot #
########################
par(mfg = c(2,1),
mar=c(0,2.15,1,0.25),
mgp=c(0,0.25,0),
cex= 0.75,
tck=-0.02,
family = "sans")
#
plot(dif1.line ~ driver1,
ylim = c(CI.mat$FIRST[2], CI.mat$FIRST[1]),
type= "n",
xlab= "",
ylab= "",
axes = F)
#
dri.ax <- pretty(range(gam.data$driver), 6)
axis(1, dri.ax, tck=-0.02,labels=F)
#
d1.ax <- pretty(c(-.85,.85)*max(abs(CI.mat$FIRST)), 6)
axis(2, d1.ax)
mtext("s'(X)",side= 2,line=1.5, cex= .75)
#
polygon(c(driver1[changepts.upper1], rev(driver1[changepts.upper1])),
c(ci1[2,][changepts.upper1], rev(as.matrix(rep(0, length(changepts.upper1)))[,1])),
col="black", border=NA)
#
polygon(c(driver1[changepts.lower1], rev(driver1[changepts.lower1])),
c(ci1[1,][changepts.lower1], rev(as.matrix(rep(0, length(changepts.lower1)))[,1])),
col="black", border=NA)
#
polygon(c(driver1, rev(driver1)),
c(ci1[2,], rev(ci1[1,])),
col = gray(0.95), border = gray(.80))
#
abline(h=0, lwd=.5)
lines(dif1.line ~ driver1, lwd=1.5)
#
# Arrow stuff should be updated ad hoc
# arrows(x0=gam.data$driver[changepts.lower1][4], y0= min(ci1[1,])*.75,
# x1=gam.data$driver[changepts.lower1][4], y1= min(ci1[1,])*.15,
# col="black",
# length=.10,
# angle=25,
# lwd=1)
#
legend("topleft",
legend="b)",
bty = "n",
box.lwd=0,
box.col="white")
#
box()
########################
# Figure C) s"(X) plot #
########################
par(mfg = c(3,1),
mar=c(2.15,2.15,1,0.25),
mgp=c(0,0.25,0),
cex= 0.75,
tck=-0.02,
family = "sans")
#
plot(dif2.line ~ driver2,
ylim = c(CI.mat$SECOND[2], CI.mat$SECOND[1]),
type= "n",
xlab= "",
ylab= "",
axes = F)
#
dri.ax <- pretty(range(gam.data$driver), 6)
axis(1, tck=-0.02,dri.ax)
mtext(dri.name, side = 1, line = 1.25, cex=0.75)
#
d2.ax <- pretty(c(-.85,.85) * max(abs(CI.mat$SECOND)), 3)
axis(2, d2.ax)
mtext('s"(X)', side= 2,line=1.5, cex= .75)
#
polygon(c(driver2[changepts.upper2], rev(driver2[changepts.upper2])),
c(ci2[2,][changepts.upper2], rev(as.matrix(rep(0, length(changepts.upper2)))[,1])),
col="black", border=NA)
#
polygon(c(driver2[changepts.lower2], rev(driver2[changepts.lower2])),
c(ci2[2,][changepts.lower2], rev(as.matrix(rep(0, length(changepts.lower2)))[,1])),
col="black", border=NA)
#
polygon(c(driver2, rev(driver2)),
c(ci2[2,], rev(ci2[1,])),
col = gray(0.95), border = gray(.80))
#
abline(h=0, lwd=.5)
lines(dif2.line ~ driver2, lwd=1.5)
#
legend("topleft",
legend="c)",
bty = "n",
box.lwd = 0,
box.col = "white")
#
box()
dev.off()
####
####
###############################################################
#Magnitude of change calculations (used to measure effect size)
###############################################################
#Below, "lower" refers to thresholds in which the lower CI of the 2nd derivative is >0 and "upper" refers to thresholds in which the upper CI is <0; "mlt" refers to the "most likely threshold value where the 2nd derivative is at its greatest value (positive or negative) within the threshold range; "start" refers to the first driver value in the threshold range and "end" refers to the last driver value in the threshold range;"1" refers to the mean of the gam line to the left of threshold, "2" refers to the mean of the gam line to the right of threshold.
#1.Identify 3 points in threshold(s) range: start, maximum value of 2nd derivative within range, and end
start.lower <- ifelse(q!=0,threshold.df.lower[1,2],NA)
mlt.lower <- ifelse(q!=0,threshold.lower.mlt[[1]],NA) #most likely threshold (mlt)
end.lower <- ifelse(q!=0,threshold.df.lower[dim(threshold.df.lower)[[1]],2],NA)
start.upper <- ifelse(p!=0,threshold.df.upper[1,2],NA)
mlt.upper <- ifelse(p!=0,threshold.upper.mlt[[1]],NA) #most likely threshold (mlt)
end.upper <- ifelse(p!=0,threshold.df.upper[dim(threshold.df.upper)[[1]],2],NA)
#2.Calculate response means and medians on both sides of threshold points using gam predicted values (i.e. gam line)
start.mean.1.lower <- mean(gam.data$response[which(gam.data$driver<start.lower)])
start.mean.2.lower <- mean(gam.data$response[which(gam.data$driver>start.lower)])
mlt.mean.1.lower <- mean(gam.data$response[which(gam.data$driver<mlt.lower)])
mlt.mean.2.lower <- mean(gam.data$response[which(gam.data$driver>mlt.lower)])
end.mean.1.lower <- mean(gam.data$response[which(gam.data$driver<end.lower)])
end.mean.2.lower <- mean(gam.data$response[which(gam.data$driver>end.lower)])
start.mean.1.upper <- mean(gam.data$response[which(gam.data$driver<start.upper)])
start.mean.2.upper <- mean(gam.data$response[which(gam.data$driver>start.upper)])
mlt.mean.1.upper <- mean(gam.data$response[which(gam.data$driver<mlt.upper)])
mlt.mean.2.upper <- mean(gam.data$response[which(gam.data$driver>mlt.upper)])
end.mean.1.upper <- mean(gam.data$response[which(gam.data$driver<end.upper)])
end.mean.2.upper <- mean(gam.data$response[which(gam.data$driver>end.upper)])
start.median.1.lower <- median(gam.data$response[which(gam.data$driver<start.lower)])
start.median.2.lower <- median(gam.data$response[which(gam.data$driver>start.lower)])
mlt.median.1.lower <- median(gam.data$response[which(gam.data$driver<mlt.lower)])
mlt.median.2.lower <- median(gam.data$response[which(gam.data$driver>mlt.lower)])
end.median.1.lower <- median(gam.data$response[which(gam.data$driver<end.lower)])
end.median.2.lower <- median(gam.data$response[which(gam.data$driver>end.lower)])
start.median.1.upper <- median(gam.data$response[which(gam.data$driver<start.upper)])
start.median.2.upper <- median(gam.data$response[which(gam.data$driver>start.upper)])
mlt.median.1.upper <- median(gam.data$response[which(gam.data$driver<mlt.upper)])
mlt.median.2.upper <- median(gam.data$response[which(gam.data$driver>mlt.upper)])
end.median.1.upper <- median(gam.data$response[which(gam.data$driver<end.upper)])
end.median.2.upper <- median(gam.data$response[which(gam.data$driver>end.upper)])
#3.Calculate proportional change on either side of threshold points
start.diff.mean.lower <- start.mean.2.lower - start.mean.1.lower
mlt.diff.mean.lower <- mlt.mean.2.lower - mlt.mean.1.lower
end.diff.mean.lower <- end.mean.2.lower - end.mean.1.lower
#
start.mag.mean.lower <- ifelse(q!=0,start.diff.mean.lower/abs(start.mean.1.lower),NA)
mlt.mag.mean.lower <- ifelse(q!=0,mlt.diff.mean.lower/abs(mlt.mean.1.lower),NA)
end.mag.mean.lower <- ifelse(q!=0,end.diff.mean.lower/abs(end.mean.1.lower),NA)
####
start.diff.mean.upper <- start.mean.2.upper - start.mean.1.upper
mlt.diff.mean.upper <- mlt.mean.2.upper - mlt.mean.1.upper
end.diff.mean.upper <- end.mean.2.upper - end.mean.1.upper
#
start.mag.mean.upper <- ifelse(p!=0,start.diff.mean.upper/abs(start.mean.1.upper),NA)
mlt.mag.mean.upper <- ifelse(p!=0,mlt.diff.mean.upper/abs(mlt.mean.1.upper),NA)
end.mag.mean.upper <- ifelse(p!=0,end.diff.mean.upper/abs(end.mean.1.upper),NA)
#
start.diff.median.lower <- start.median.2.lower - start.median.1.lower
mlt.diff.median.lower <- mlt.median.2.lower - mlt.median.1.lower
end.diff.median.lower <- end.median.2.lower - end.median.1.lower
#
start.mag.median.lower <- ifelse(q!=0,start.diff.median.lower/abs(start.median.1.lower),NA)
mlt.mag.median.lower <- ifelse(q!=0,mlt.diff.median.lower/abs(mlt.median.1.lower),NA)
end.mag.median.lower <- ifelse(q!=0,end.diff.median.lower/abs(end.median.1.lower),NA)
####
start.diff.median.upper <- start.median.2.upper - start.median.1.upper
mlt.diff.median.upper <- mlt.median.2.upper - mlt.median.1.upper
end.diff.median.upper <- end.median.2.upper - end.median.1.upper
#
start.mag.median.upper <- ifelse(p!=0,start.diff.median.upper/abs(start.median.1.upper),NA)
mlt.mag.median.upper <- ifelse(p!=0,mlt.diff.median.upper/abs(mlt.median.1.upper),NA)
end.mag.median.upper <- ifelse(p!=0,end.diff.median.upper/abs(end.median.1.upper),NA)
#
resp.start.lower <- ifelse(q!=0,threshold.df.lower[[1,1]],NA)
resp.mlt.lower <- ifelse(q!=0,threshold.lower.mlt[[2]],NA)
resp.end.lower <- ifelse(q!=0,threshold.df.lower[[dim(threshold.df.lower)[1],1]],NA)
dri.start.lower <- ifelse(q!=0,threshold.df.lower[[1,2]],NA)
dri.end.lower <- ifelse(q!=0,threshold.df.lower[[dim(threshold.df.lower)[1],2]],NA)
resp.start.upper <- ifelse(p!=0,threshold.df.upper[[1,1]],NA)
resp.mlt.upper <- ifelse(p!=0,threshold.upper.mlt[[2]],NA)
resp.end.upper <- ifelse(p!=0,threshold.df.upper[[dim(threshold.df.upper)[1],1]],NA)
dri.start.upper <- ifelse(p!=0,threshold.df.upper[[1,2]],NA)
dri.end.upper <- ifelse(p!=0,threshold.df.upper[[dim(threshold.df.upper)[1],2]], NA)
magnitude <- as.data.frame(cbind(resp.name,
dri.name,
resp.start.lower, #response value at beginning of threshold
resp.mlt.lower, #response value at most likely threshold value
resp.end.lower, #response value at end of threshold
start.lower, #driver value at beginning of threshold
mlt.lower, #driver value where 2nd derivative is furthest away from 0
end.lower, #driver value at end of threshold
start.mag.mean.lower, #magnitude of response across the threshold at start of threshold range
mlt.mag.mean.lower, #magnitude of response across the threshold at most likely threshold value of threshold range
end.mag.mean.lower, #magnitude of response across the threshold at end of threshold range
start.mag.median.lower, #magnitude of response across the threshold at start of threshold range
mlt.mag.median.lower, #magnitude of response across the threshold at most likely threshold value of threshold range
end.mag.median.lower, #magnitude of response across the threshold at end of threshold range
resp.start.upper, #response value at beginning of threshold
resp.mlt.upper, #response value at most likely threshold value
resp.end.upper, #response value at end of threshold
start.upper, #driver value at beginning of threshold
mlt.upper, #driver value where 2nd derivative is furthest away from 0
end.upper, #driver value at end of threshold
start.mag.mean.upper, #magnitude of response across the threshold at start of threshold range
mlt.mag.mean.upper, #magnitude of response across the threshold at most likely threshold value of threshold range
end.mag.mean.upper, #magnitude of response across the threshold at end of threshold range
start.mag.median.upper, #magnitude of response across the threshold at start of threshold range
mlt.mag.median.upper, #magnitude of response across the threshold at most likely threshold value of threshold range
end.mag.median.upper #magnitude of response across the threshold at end of threshold range
))
colnames(magnitude)<-c("Response","Driver","Response.start.lower","Response.mlt.lower","Response.end.lower","Threshold.start.lower","Most.likely.threshold.lower","Threshold.end.lower","Mean magnitude.start.lower","Mean magnitude.mlt.lower","Mean magnitude.end.lower","Median magnitude.start.lower","Median magnitude.mlt.lower","Median magnitude.end.lower","Response.start.upper","Response.mlt.upper","Response.end.upper","Threshold.start.upper","Most.likely.threshold.upper","Threshold.end.upper","Mean magnitude.start.upper","Mean magnitude.mlt.upper","Mean magnitude.end.upper","Median magnitude.start.upper","Median magnitude.mlt.upper","Median magnitude.end.upper")
allMagnitude <- rbind(allMagnitude,magnitude)
resp.name <- NULL
dri.name <- NULL
}
write.csv(allMagnitude,paste0(results.dir,paste0(dataset,'.magnitude of threshold.gamm.csv')),row.names=F)
allMagnitude = NULL
####################################################################################################################
###CODE FOR MAKING PLOTs FOR RELATIONSHIPS THAT SHOWED GAM WAS THE BEST MODEL (using "pick.gam" from line 353 above)
####################################################################################################################
###############################################################################################################
## Changes from the GAMM bootstrapping and plotting above include:
## 1)Using gam instead of gamm
## 2)Remove gaussian bootstrap process, but use the resids from myresponse~gam1$fitted (this is different from Scott's original code). Using the resids gives CI around the gam fit that look more believable.
###############################################################################################################
for(row.i in pick.gam) {
resp.name <- as.character(bestList$RESPONSE[row.i])
dri.name <- as.character(bestList$DRIVER[row.i])
dat.cut <- dat.full[colnames(dat.full) %in% c("year", resp.name, dri.name)]
dat.cut <- dat.cut[apply(dat.cut, 1, function(x)!any(is.na(x))),]
#
myresponse <- dat.cut[[resp.name]]
mydriver <- dat.cut[[dri.name]]
ts.length <- dat.cut$year
gam1 <- gam(myresponse ~ s(mydriver, bs = "tp", k = ks), method = "GCV.Cp", se = T)
ind.fit <- list(mydriver = seq(from = min(mydriver), to = max(mydriver), length.out = sp.len))
pred <- predict.gam(gam1, newdata = ind.fit, type = "response", se.fit = T)
#
gam.data <- data.frame(pred$fit,
ind.fit$mydriver)
colnames(gam.data) <- c("response","driver")
# Bootstrap and subsequent code in a nutshell...
# 1) take a random sample of the data 1000 times
# 2) take GAM of each bootstrap replicate (br)
# 3) Take the 1st and 2nd derivative of each br
# 4) When 95% of the 1st or 2nd derivative replicates are greater or less than zero, we have a significant